Cowan's Codes: General description

This file is prepared by L. Kocbach, University of Bergen, on the basis of R. Cowan's file readme (at t4.lanl.gov/pub/cowan/) contained in the standard distribution. of Cowan's code. WARNING: Do not edit this file using Netscape Composer newer than 3.0 !!!! (or any other similar programs) They will destroy the data below!!

In Cowan's standard distribution, the programs are called rcn rcn2 rcg rce This suite of four programs calculates atomic structures and spectra via the superposition-of-configuration method:

(1) RCN calculates one-electron radial wavefunctions (bound or free) for each of any number of specified electron configurations, using the Hartree-Fock or any of several more approximate methods. The principal output, for each configuration, consists of the center- of-gravity energy (Eav) of the configuration, and those radial Coulomb (Fk and Gk) and spin-orbit (zeta) integrals required to calculate the energy levels for that configuration.

(2) RCN2 is an interface program that uses the output wave- functions from RCN (on a file called tape2n) to calculate the configuration-interaction Coulomb integrals (Rk) between each pair of interacting configurations, and the electric-dipole (E1) and/or electric quadrupole (E2) radial integrals between each pair of configurations. RCN2 prepares an output file called out2ing that (after being renamed ing11) serves as input to RCG.

(3) RCG sets up energy matrices for each possible value of the total angular momentum J, diagonalizes each matrix to get eigenvalues (energy levels) and eigenvectors (multi-configuration, intermediate- coupling wavefunctions in various possible angular-momentum-coupling representations), and then computes M1 (magnetic dipole), E2, and/or E1 radiation spectra, with wavelengths, oscillator strengths, radiative transition probabilities, and radiative lifetimes. Other options, when a continuum (free) electron is present, are photoionization cross- sections, autoionization transition probabilities, total lifetimes, branching ratios for autoionization, and plane-wave Born collision strengths.

(4) When higher accuracy results are desired, RCE can be used to vary the various radial energy parameters Eav, Fk, Gk, zeta, and Rk to make a least-squares fit of experimental energy levels by an iterative procedure. The resulting least-squares-fit parameters can then be used to repeat the RCG calculation with the improved energy levels and (presumeably) wavefunctions.

Reference: Robert D. Cowan, "The Theory of Atomic Structure and Spectra," (University of California Press, Berkeley, 1981), esp. Chapters 8 and 16.

rcn input

A detail discussion of the input of the first program rcn in the suite is described in detail in this document.

rcn2 input

The two-card input for the rcn2 program is more-or-less universally of the form g5inp 000 0.0000 00 339099909090 0.00 07229 -1 The items on the control card will not be described in detail, but some information is given here.

if either digit in the "00" is made non-zero, then eigenvectors in the LS or jj-coupling representation, respectively, will not be printed in RCG;

the "33" calls for M1 and E2 spectra, respectively, to be calculated in RCG for both parities (zeros will delete these),

"7" calls for print in RCG of the spectrum line list sorted by first- parity energy levels, by second-parity energies, and by wavenumber (inverse wavelength);

1, 2, or 4 instead of 7, prints only one of these sorts,

and a 3 or 6 will print two of them.

The "9099909090" represent 2-digit scale factors (in percent, 99 representing 100%) for respectively

Fk between equivalent electrons,

spin-orbit parameters,

Fk and Gk for non-equivalent electrons,

and configuration-interaction Rk radial integrals:

It is known empirically that scaling down of the HF Coulomb radial integral values by 5 to 30 percent will give RCG eigenvalues in better agreement with experimental energy levels, the smaller factors being for neutral or weakly ionized systems, with factors approaching unity being appropriate for highly ionized systems.

The input for the rcg program

The input for the rcg program is based on the output of the rcn2 program.

Output from rcn2 consists of print output in file out2 and a file out2ing that, renamed ing11, forms an input file for the rcg program.

With the three K VI configurations used as input for RCN, this file (with "33" on the rcn2 control card replaced by "00" or "30") will be 3 10e-350e05 000005 10. 0 5.0 2.0 1.0 0.5 0.2 0 0000000000 1000.0000 1 03 2 23 1 10 00 0 1000.0000 0.00 1 07-6 0 0 s 2 p 2 s 0 s 0 s 0 s 0 s 0 s 0 k vi 3s2 3p2 -130337.379 0.0000 s 0 p 4 s 0 s 0 s 0 s 0 s 0 s 0 k vi 3p4 -129993.306 0.0000 s 2 p 1 d 1 s 0 s 0 s 0 s 0 s 0 k vi 3p 3d -130106.201 0.0000 k vi 3s2 3p2 3 00 7609731 178682 00 00hf90999090 k vi 3p4 3 34407320 7574361 178422 00 00hf90999090 3s2 3p2 -3p4 1 101.64285 0.00005 0.00005 0.00005 0.00005hf90999090 k vi 3p 3d 6 23117760 180352 8932 7177693 8834344hf90999090 5512094 k vi 3s2 3p2 k vi 3p 3d 1.70752( 3p//r1// 3d)-0.990hf -92 -96 k vi 3p4 k vi 3p 3d 0.00000( //r1// )0.0000hf 0 0 -99999999. -1 except that the first two (optional) control cards will be absent (but can be edited in), and except that the "-6" in columns 73-74 of the principal control card will be zero if a zero was used in columns 71-75 of the RCN control card. (As in RCN, the value -6 causes intermediate calculational output to be sent to the monitor screen during the course of the RCG calculation.)

Here the Eav values in ry from RCN

(-1197.769, 1184.586, and 1185.615, resp.) have been changed by RCN2 to values in kK (-130337.379, etc.),

and then to values 0.0, 344.0732, and 231.1776 kK relative to the value for the first configuration. Values of the other radial energy integrals have been scaled down by the factors 0.90, 1.00, 0.90, etc., and are in kK, which will then be the units of energy-matrix elements and eigenvalues, unless the "1000.0000" on the second optional control card is changed--for example, to 8065.48 to obtain all energies in eV.

(The "0000000000" on the second optional control card can be replaced by non-zero values to change the scale factors from the ones specified on the RCN2 control card to these new values.)

NOTE: For a first RCG calculation, the input file must consist of (or begin with) a set of coefficient-of-fractional-parentage decks for each set of subshells (e.g., s0, s1, s2, p0, p1, p2,...) that will be involved in any of the configurations for which calculations are to be made. (Decks are not needed for singly occupied subshells if there will be no more-highly occupied subshells of the same l.) The file ing11k contains such a set of cfp decks, and can be used for this first calculation to compute files tape72, tape73, and tape74 for use in subsequent RCG calculations. [Some IBM systems do not allow file numbers greater than 50; for these systems, the "72" on the first line of ing11k can be changed to "42" to produce files tape42, tape43, and tape44, the statement id2def=72 near the beginning of the main program of RCG correspondingly changed to id2def=42, and the OPEN statements for units 72, 73, and 74 likewise changed appropriately.]

NOTE: The file rcng.UNIX is a c-shell procedure file for automatically running rcn rcn2 rcng in succession on UNIX-type systems.

If it is launched by the command
rcng.UNIX .KVI
the three output files will be named
out36.KVI, out2.KVI, and outg11.KVI .

The file rcng.VMS is a similar command file for VMS systems; for usage, see the file RCNwriteup.

The c-shell script rcng.UNIX

Note that the script provided in the distribution will crash. I have corrected it (L. Kocbach) by including the values of parameters which are in fact correctly listed in the file OutputK+5

In case that the browser garbles the following script, it is linked here in its pure text form rcng.UNIX #!/bin/csh -f rm in36 in2 ing11 inputg cat < in36 2 -9 2 10 0.2 5.e-08 1.e-11-2 090 1.0 0.65 40.0 0.0 -6 19 6K VI 3p2 3s2 3p2 19 6K VI 3p4 3p4 19 6K VI 3p 3d 3s2 3p 3d -1 eod36 rcn cat << eod2 > in2 g5inp 000 0.000 00 009099909090 0.00 07229 -1 eod2 rcn2 mv out36 out36$1 mv out2 out2$1 cat < inputg 3 10e-350e05 000005 10. 0 5.0 2.0 1.0 0.5 0.2 0 0000000000 1000.0000 eodg cat inputg out2ing >> ing11 rcg mv outg11 outg11$1



rce input

If on the RCG control card a

-1

is placed in columns 9-10

and the card containing "-99999999."

is preceded with an identical card, except with 5's instead of 9's,

then rcg will write a binary file tape2e and a BCD file outgine . If the name of the latter is changed to ine20, the rce program can be run with the RCG energy parameters and theoretical energy levels as input.

The rce program should then converge straightforwardly in about three cycles with little or no change in parameter values, which then provides a test run for the RCE code.

Genuine RCE runs require that experimental energy levels be edited by hand into ine20 in place of the theoretical eigenvalues.

An RCE output file parvals contains final least-squares parameter values, which can be edited into the rcg input file ing11 for a repeat run with the new parameter values.

Program writeups

Various possible additional RCG options can be input on the RCN2 control card and carried over automatically to RCG, or entered directly onto the RCG control card, but they are too numerous and detailed to describe here. Likewise, notes on convergence problems, etc., in RCN and RCE will not be given here. For details, see the hard-copy program writeups available from the author upon request:

e-mail to Robert D. Cowan: rcowan@lanl.gov

or regular post to Robert D. Cowan 2917B Nickel Los Alamos, NM 87544 USA phone (505)-662-4095.

Note: ASCII versions of the writeups are included in the ftp directory; they are useful to a certain extent, but are somewhat difficult to read, because there are no sub- nor superscripts, Greek letters, nor script letters for coupled quantum numbers LSJ. There are no sample output listings in the RCN and RCG writeups, but these are contained in files OutputK+5 and OutputSe+24 for a normal dipole-spectrum run in K VI and a dielectronic-recombination calculation in Se XXV.


This file is prepared by L. Kocbach, University of Bergen, on the basis of R. Cowan's file readme (at t4.lanl.gov/pub/cowan/) contained in the standard distribution. of Cowan's code.